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Articles 61 - 61 of 61
Full-Text Articles in Discrete Mathematics and Combinatorics
A Combinatorial Model For Affine Demazure Crystals Of Levels Zero And One, Samuel Spellman
A Combinatorial Model For Affine Demazure Crystals Of Levels Zero And One, Samuel Spellman
Electronic Theses & Dissertations (2024 - present)
The symmetric and non-symmetric Macdonald polynomials are special families of orthogonal polynomials with parameters q and t. They are indexed by dominant, (resp. arbitrary) weights associated to a root system and generalize several well-known polynomials such as the Schur polynomials, Jack polynomials, Hall-Littlewood polynomials, etc. There are two well-known combinatorial models for computing these polynomials: a tableau model in type A, due to Haglund, Haiman and Loehr, and a type-independent model due to Ram and Yip, based on alcove walks.
Crystals bases are an important construction encoding information about Lie algebra representations. It turns out that there is an interesting …